Off-topic: Personally I think Shakespeare was a hack who got very lucky.
On-topic: There are minor differences in certain passages. I don't have the list in front of me at the moment, and I don't really care to look it up, but the biggest difference is that the King James Version has some of the laws regarding divorce slightly modified. This was done so that some old king could divorce his wife (hence, King James Bible). Now, if you're thinking to yourself "doesn't the bible have rules against editing it?" Well, yes, which is why the New King James Version reverts those changes but preserves the archaic words. Future translations like NIV are based on the NKJV, not the KJV.
As for why fundies insist on the KJV and not the NKJV... fuck if I know.